Absorption and Transport Effects Induced in Plasmas by the Interaction of Electrons with Laser Speckles

We show that the ponderomotive force associated with laser speckles can scatter electrons in a laser-produced plasma in a manner similar to Coulomb scattering. Analytic expressions for the effective collision rates are given. The electron-speckle collisions become important at high laser intensity or during filamentation, affecting both long- and short-pulse laser intensity regimes. As an example, we find that the effective collision rate in the laser-overlap region of hohlraums on the National Ignition Facility is expected to exceed the Coulomb collision rate by 1 order of magnitude, leading to a fundamental change to the electron transport properties. At the high intensities characteristic of short-pulse laser-plasma interactions ($I\gtrsim {10}^{17}\mathrm{W}{\mathrm{cm}}^{-2}$), the scattering is strong enough to cause the direct absorption of laser energy, generating hot electrons with energy scaling as $E\approx 1.44{(I/{10}^{18}\mathrm{W}{\mathrm{cm}}^{-2})}^{1/2}\mathrm{MeV}$, close to experimentally observed results.

Figure 1

A simple hohlraum illuminated by two speckled laser beams (with incident $k$ vectors ${\mathbf{k}}_1$ and ${\mathbf{k}}_2$). Speckles approximated with cylindrical (“cyl.”) and spherical (“sph.”) symmetry are shown. The colorbar corresponds to the laser intensity (normalized to the average), and the cyan curve (labeled “e”) shows an example electron trajectory.

Figure 2

The speckle collision rate relative to the Coulomb rate (${\nu }_{p,c,M}/{\upsilon }_{ei}$) as a function of laser intensity. The intensity in the laser overlap region on the NIF is indicated by the asterisk (*). The dashed red line corresponds to the same conditions as the red line but accounts for thermal filamentation.

Figure 3

The electric field ($E_x$) that results from the interference of an incident Gaussian plane wave (moving in the $z$ direction) reflecting off a nonuniform critical surface.

Figure 4

(a) Average electron energy as a function of time and (b) final electron energy spectrum for two interfering 300 fs pulses with peak intensity $4\times {10}^{17}\mathrm{W}{\mathrm{cm}}^{-2}$ and ${\lambda }_0=1\mu \mathrm{m}$.

Figure 5

Hot electron energy scaling with intensity from simulations with 300 fs pulses (black dots). The ponderomotive scaling is shown in red, alongside our analytic expression $E\approx 1.44{(I/{10}^{18}\mathrm{W}{\mathrm{cm}}^{-2})}^{1/2}\mathrm{MeV}$ in blue and recent experiments (green).

Figure 6

Schematic diagram showing the key parameters in the analytic treatment of an electron interacting with a speckle of radius $R$.